A lot of stuff written on UK interest rates reasons as follows. Many estimates of the UK’s output gap - the difference between actual output and the level of output that is consistent with steady (domestically generated) inflation - suggest it is almost zero. That cannot be consistent with nominal short term interest rates as low as 0.5%. Therefore a rise in interest rates is long overdue.
This ignores the rest of the world. Although the OECD estimate that the UK output gap in 2015 is zero, they also estimate it is nearly -2% for the OECD as a whole and nearly 3% for the Euro area. That means the UK is selling less goods abroad. For the UK output gap to be zero, we therefore need some other element of UK aggregate demand to take up the slack created by low exports. It is not government spending, which is going in the opposite direction. So it is consumers and firms that have to be encouraged to borrow more and save less. To put it another way, they need to be encouraged to shift spending from the future to the present. That means lower than normal UK real interest rates.
It is still true that monetary policy should be easier in the Eurozone than in the UK, but with active QE it already is. The fact that markets expect UK interest rates to rise well before those in the Eurozone intensifies the exports problem, because it means that exports are being hit not just by low demand but also by becoming less competitive as sterling appreciates against the Euro. 
The problem of low demand for UK exports would be made worse still if, as I suspect, sterling is overvalued even after you allow for differences in expected interest rates. Philip Lane, soon to become governor of the Irish central bank, has produced an interesting analysis of the recent deterioration in the UK current account. He concludes that “financial engineering may have played some role”. I suspect he is right, mainly because he is a renowned expert on these matters. However I wanted to stress that my arguments about overvaluation owed nothing to this recent deterioration.
The UK’s trade balance deficit has remained large and fairly constant for many years, despite the depreciation around 2008. That was not offset by investment income, even before the recent deterioration, which is why we have been running current account deficits for over 15 years. There may be good reasons why some countries run deficits for a long period of time, but it is not obvious whether any of these reasons apply to the UK, and those deficits in themselves mean that the equilibrium exchange rate will be depreciating alongside those deficits.
So we should not expect UK real interest rates to return to their ‘normal’ level until output gaps are closed in the rest of the world. We should also note that the Bank thinks that the normal or natural level of real interest rates is much less than it has been in the past (secular stagnation). Finally with inflation currently low, low real interest rates imply low nominal rates. All this would be true even if you were certain that the current UK output gap was zero, which I am not.
 Using UIP, the current real exchange rate is determined by the medium term equilibrium rate (calculated at zero output gaps everywhere) plus expected real interest rate differentials.